processes and constraints in scientific model construction
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Processes and Constraints in Scientific Model Construction. Will Bridewell † and Pat Langley †‡ † Cognitive Systems Laboratory, CSLI, Stanford University ‡ CIRCAS, Arizona State University. Where Are We Going?. Introduction to inductive process modeling - PowerPoint PPT PresentationTRANSCRIPT
PROCESSES AND CONSTRAINTS IN
SCIENTIFIC MODEL CONSTRUCTION
Will Bridewell† and Pat Langley†‡
†Cognitive Systems Laboratory, CSLI, Stanford University
‡CIRCAS, Arizona State University
Where Are We Going?
Introduction to inductive process modeling
Constraints in inductive process modeling
Learning constraints
Inductive Process Modeling
Observations PredictionsModel
Model Objectives: Explanation and PredictionLangley et al. 2002, ICML; Bridewell et al.
2008, ML
• Ordinary Differential Equations
• Processes
Quantitative Process Models
process exponential_growth equations d[hare.density, t, 1] = 2.5 * hare.density
process exponential_loss equations d[wolf.density, t, 1] = −1.2 * wolf.density
process predation_holling_type_1 equations d[hare.density, t, 1] = −0.1 * hare.density * wolf.density d[wolf.density, t, 1] = 0.3 * 0.1 * hare.density * wolf.density
dhare.density/dt = 2.5 * hare.density + −0.1 * hare.density * wolf.densitydwolf.density/dt = −1.2 * wolf.density + 0.3 * 0.1 * hare.density * wolf.density
Advantages of Quantitative Process Models
Process models offer scientists a promising framework because:
· they embed quantitative relations within qualitative structure;
· that refer to notations and mechanisms familiar to experts;
· they provide dynamical predictions of changes over time;
· they offer causal and explanatory accounts of phenomena;
· while retaining the modularity needed for induction/abduction.
Quantitative process models provide an important alternative to formalisms used currently in computational discovery.
• Ordinary Differential Equations
• Processes
Modularity in Quantitative Process Models
process exponential_growth equations d[hare.density, t, 1] = 2.5 * hare.density
process exponential_loss equations d[wolf.density, t, 1] = −1.2 * wolf.density
process predation_holling_type_1 equations d[hare.density, t, 1] = −0.1 * hare.density * wolf.density d[wolf.density, t, 1] = 0.3 * 0.1 * hare.density * wolf.density
dhare.density/dt = 2.5 * hare.density + −0.1 * hare.density * wolf.densitydwolf.density/dt = −1.2 * wolf.density + 0.3 * 0.1 * hare.density * wolf.density
• Ordinary Differential Equations
• Processesprocess exponential_growth equations d[hare.density, t, 1] = 2.5 * hare.density
process exponential_loss equations d[wolf.density, t, 1] = −1.2 * wolf.density
dhare.density/dt = 2.5 * hare.densitydwolf.density/dt = −1.2 * wolf.density
Modularity in Quantitative Process Models
• Ordinary Differential Equations
• Processesprocess exponential_growth equations d[hare.density, t, 1] = 2.5 * hare.density
process exponential_loss equations d[wolf.density, t, 1] = −1.2 * wolf.density
process predation_holling_type_2 equations d[hare.density, t, 1] = −0.1 * hare.density * wolf.density / (1 + 0.2 * –0.1 * hare.density) d[wolf.density, t, 1] = 0.3 * 0.1 * hare.density * wolf.density / (1 + 0.2 * –0.1 * hare.density)
dhare.density/dt = 2.5 * hare.density + −0.1 * hare.density * wolf.density / (1 + 0.2 * –0.1 * hare.density)dwolf.density/dt = −1.2 * wolf.density + 0.3 * 0.1 * hare.density * wolf.density / (1 + 0.2 * –0.1 * hare.density)
Modularity in Quantitative Process Models
Generic Processesgeneric process predation_Holling_1 entities P1{prey}, P2{predator} parameters r[0, infinity], e[0, infinity] equations d[P1.density, t, 1] = −1 * r * P1.density * P2.density d[P2.density, t, 1] = e * r * P1.density * P2.density
Generic Processesgeneric process predation_Holling_1 entities P1{prey}, P2{predator} parameters r[0, infinity], e[0, infinity] equations d[P1.density, t, 1] = −1 * r * P1.density * P2.density d[P2.density, t, 1] = e * r * P1.density * P2.density
InstantiationP1: hare P2: wolf
r: 0.1 e: 0.3
Generic Processesgeneric process predation_Holling_1 entities P1{prey}, P2{predator} parameters r[0, infinity], e[0, infinity] equations d[P1.density, t, 1] = −1 * r * P1.density * P2.density d[P2.density, t, 1] = e * r * P1.density * P2.density
process wolves_eat_hares equations d[hare.density, t, 1] = −1 * 0.1 * hare.density * wolf.density d[wolf.density, t, 1] = 0.3 * 0.1 * hare.density * wolf.density
InstantiationP1: hare P2: wolf
r: 0.1 e: 0.3
The IPM System• Given:
- A library of generic entities and processes- Instantiated entities- Data
Ground the generic processes with instantiated entities Generate all combinations of the ground
processes Fit the numeric parameters of each structure
• Output: The best models based on fit to the data
(a naive approach)
Applications
Aquatic Ecosystems Fjord Dynamics
also, biochemical kinetics, protist interactions, photosynthesis
See Bridewell et al. 2008, Machine Learning, 71, 1–32
Life After IPM
• help scientists formalize their modeling knowledge;
• let scientists consider several alternative models;
• reduce some of the drudgery of model construction;
• speed exploration and evaluation.
Early versions of inductive process modeling systems:
However, IPM produces several structurally implausible models, some of which account quite well for the data.
Model Constraints
eliminate implausible models;
reduce the size of the search space;
make complex domains tractable;
improve model accuracy during incomplete search.
HIPM, Todorovski et al. AAAI-05
Constraints on the structure of models:
Structural constraints differ from constraints on model behavior most importantly because they do not require simulation.
SC-IPM Constraints: Necessary
Name: Nutrient-ReplenishmentType: necessaryProcesses: nutrient_mixing(N), remineralization(N,_ )
Specifies Required Processes
P = primary producerG = grazerN = nutrient
Name: Growth-LimitationType: always-togetherProcesses: limited(P), nutrient_limitation(P, N)
All or None
P = primary producerG = grazerN = nutrient
SC-IPM Constraints: Always-Together
Name: Growth-AlternativesType: exactly-oneProcesses: exponential(P), logistic(P), limited(P)
Mutual Exclusion
P = primary producerG = grazerN = nutrient
SC-IPM Constraints: Exactly-One
Name: Optional-GrazingType: at-most-oneProcesses:
holling_1(P,G), holling_2(P,G), holling_3(P,G)
Enables Optional Processes
P = primary producerG = grazerN = nutrient
SC-IPM Constraints: At-Most-One
The SC-IPM System1. Ground the generic processes with instantiated
entities.
2. Treat ground processes as Boolean literals.
3. Conjoin the individual constraints.
4. Rewrite the constraints in conjunctive normal form.
5. Apply a SAT solver (e.g., DPLL,WalkSAT).
6. Instant model structure!
7. Fit parameters, etc.
Advantages of SC-IPM
• constraints that limit the consideration of implausible models;
• constraint modularity that eases control of the search space.
SC-IPM adds several powerful features to IPM, such as:
The constraints used by SC-IPM typically come from a scientist’s implicit knowledge, and we can both elicit them through examples and learn them computationally.
Goal:Identify implicit or unknown constraintsto use in future modeling tasks
Plan:Analyze the space of model structuresUse machine learning techniques to help
Key Idea:Don’t throw away any modelsEven the bad ones contain valuable
information
Learning Constraints
Bridewell & Todorovski 2007, ILP and KCAP
Learning Constraints1. Build and parameterize process models
2. Store the models for analysis
3. Formally describe the structure of the models
4. Identify good and bad models
5. Use ILP to generate descriptions of accurate and inaccurate model structures
6. Convert the descriptions into SC-IPM constraints
We chose Aleph by Ashwin Srinivasan due to its ready availability and capabilities.
Good and Bad Models
1996–1997 Ross Sea
Good Bad
Extracted ConstraintsA model that includes a second-order exponential mortality process for phytoplankton will be inaccurate. (positive:560, negative: 0)
A model that includes the Lotka–Volterra grazing process will be inaccurate. (positive: 80, negative: 0)
A model that lacks both the first and second order Monod growth limitation process between iron and phytoplankton will be inaccurate. (positive: 448, negative: 0)
Apply Constraints to Other Problems
Ross Sea Across YearsSearch Spaces: 9x–16x smallerModel Distribution: more accurate
Apply Constraints toOther Domains
Ross Sea to Bled Lake
Bridewell & Todorovski AAAI-08 (Transfer Learning Workshop)
Related Work Other quantitative modelers
LAGRAMGE (Todorovski & Dzeroski)
PRET (Bradley & Stolle)
Metalearning and others
Learning Constraint Networks via Version Spaces (Bessiere et al.)
Relational Clichés (Silverstein & Pazzani; Morin & Matwin)
Mode Declarations in ILP (McCreath & Sharma)
Rule Reliability from Prior Performance (Mark Reid)
• continuing the analysis of constraint transfer;
• closing the automated modeling + constraint learning loop;
• basing new analyses and methodologies on model ensembles;
• adapting the general strategies to other tasks;
• supporting other modeling paradigms.
Future Directions
We are currently working in several directions which include:
Inductive process modeling is a fruitful paradigm for exploring knowledge representation, modeling, discovery, and creativity in scientific practice.